TELKOMNIKA ISSN: 1693-6930
Low Complexity Selective Adaptive Multicarrier DS-CDMA Receiver Ahmed El-Sayed El- Mahdy
325 Where
k ii,
ρ
is the correlation coefficient between the signature waveforms of the user of interest k=ii and the user k for the uth subcarrier.
3. Low complexity Selective Adaptive Parallel Interference Cancellation
The selective APIC is based on dividing users signals into reliable and unreliable signals. The
M
outputs of matched filter bank
k m
p
u
,
corresponding to the identical-bit streams are combined together using MRC, the soft output of MRC
k
u
Z
is compared to a suitable threshold value
S
to decide whether it’s tentatively decision
k u
bˆ
=
sgn
k
u
Z
is reliable or not, the output of the threshold comparator
k u
a ~
can be written as equation 7.
, ,
1 ,
1 ~
S
Z S
Z S
S Z
a
k k
k k
u
u u
u
7
If
k u
a ~
=1,
k u
bˆ
is decided to be reliable otherwise,
k u
bˆ
is decided to be unreliable. The reliable signals are directly detected, while the unreliable signals are further processed with APIC
scheme to get more re-estimate for them. In order to further illustrate this procedure let us assume that without loss of generality users
l k
,....., 3
, 2
, 1
are reliable, i.e.,
S Z
k v
u
,
for,
l k
1
while the other users
K l
k ,......,
1
are unreliable, also the user ii is considered unreliable. The reconstructed signal of the kth user, uvth subcarrier, and n
th
chip is given by equation 8.
ˆ cos
2 ˆ
n c
b g
M P
n I
k k
u k
uv k
uv k
uv
ϕ
8 The sum of all reconstructed reliable signals
l k
,....., 3
, 2
, 1
is subtracted from
n r
uv
to get
n r
uv
which will be used as a reference signal to determine suboptimum weight for each unreliable signal. After subtracting the reconstructed reliable signals, APIC scheme will be
applied as follows; the reconstructed signals of unreliable users are multiplied by their corresponding adaptive weights
n w
k uv
and summed together to produce an estimate
ˆ n
r
uv
of the reference signal
n r
uv
, which can be expressed as equation 9.
K l
k k
uv k
uv uv
N n
n w
n I
n r
1
1 .
ˆ ˆ
9 The difference between
n r
uv
and
ˆ n
r
uv
constitute the MAI estimation error for unreliable signals, based on this error, a cost function of the adaptive algorithm can be defined as
equation 10.
, ˆ
2 2
n r
n r
E n
e E
uv uv
uv uv
ε
10
ISSN: 1693-6930
TELKOMNIKA Vol. 11, No. 2, June 2013: 321 – 330
326 Where E [.] is the statistical expectation operator and
n
e
uv
ˆ n
r n
r
uv uv
is the error of the MAI
estimation. In order to minimize the cost function, the weights
n w
k uv
are updated at the chip rate according to the Normalized LMS NLMS algorithm as equation 11
], :
1 [
, ]
[ ]
ˆ [
ˆ .
1
2 1
K l
k n
e I
I n
w n
w
uv k
uv K
l k
k uv
k uv
k uv
µ
11 Where
µ
denotes the step-size, and initial value of weight
k uv
w
of value 0 or 1. At the end of one transmission interval bit the determined weight
1
N w
k uv
is used with the next stage PIC to obtain final decision for the unreliable signals. At PIC stage, sub-
optimal weights
, 1
N
w
k uv
are used to weight the input signal
ˆ n
I
k uv
over the entire transmission interval bit. Subtracting the weighted MAI, the cleaner signal for the user ii is
given by equation 12
K l
k k
uv uv
ii uv
ii k
n v
n r
n x
1
, ˆ
12 Where
ˆ n
v
k uv
is given by equation 13.
, 1
ˆ ˆ
N w
n I
n v
k uv
k uv
k uv
for
. :
1 K l
k
. 13
The signal
ii uv
x
is then passed to the matched filter bank and the M outputs of matched filter bank are combined via MRC. The final decision for the unreliable signals is obtained
according to equation 14.
. ]}
[ {
sgn ~
1 1
N n
ii uv
ii M
m ii
uv ii
u
g n
c n
x b
14 After performing SA-PIC for unreliable signals, the final decision for all users are
obtained as
u
bˆ
=
l
k k
u
b
1
ˆ
+
, ~
1
K l
k k
u
b
Where the first term represents the estimated data from the first stage MF, while the second term represents the re-estimated data after APIC.
4. Computer Simulations and Results
